self-balanced hand rankings

[Losing all]

I would guess ace/little goes up due to the fact that no self respecting player will fold their BB to an allin by an aggeressive player if they hold kj or the like.

Since were on the subject, I was wondering last night about how big a favorite top card/bottom card was to two middle cards. assume no flush or straight draws, something like A6o vs k7o?

[Nottom]

[ QUOTE ]
Since were on the subject, I was wondering last night about how big a favorite top card/bottom card was to two middle cards. assume no flush or straight draws, something like A6o vs k7o?

[/ QUOTE ]

These are normally in the 60-40 range

From twodimes:
pokenum -h ac 6d - ks 7h
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Ac 6d 1026088 59.92 680824 39.76 5392 0.31 0.601
Ks 7h 680824 39.76 1026088 59.92 5392 0.31 0.399

[Dave Holdsworth]

Since you have taken the top 50% of hands (or 45% actually) then that group must include a fair number of large cards lower than A, such as Kx, Qxs (higher in proportion than the top 15% or in the top 100%). Given that, I would expect A2o to rise in value which seems to be the case.

I guess if you took the top 15% self-corrected the A2o would go back down again.

[Losing all]

Thanks. I was thinking it was a little less (like 58/42) good to know.

[dana33]

You expressed some doubt about the correctness of your results, but I have done my own calculations which exactly match yours. I also did the self-balanced calculation for the top 25% of hands (top 42 to be precise), which took a few more iterations to converge than the 50% case. My results are as follows for the top 84 hands in each case:

vs random vs top 84 vs top 42
AA 0.8520 AA 0.8528 AA 0.8501
KK 0.8240 KK 0.7864 KK 0.7406
QQ 0.7993 QQ 0.7327 QQ 0.6966
JJ 0.7747 JJ 0.6990 JJ 0.6580
TT 0.7501 TT 0.6699 AKs 0.6243
99 0.7206 AKs 0.6692 TT 0.6210
88 0.6916 AKo 0.6528 AKo 0.6059
AKs 0.6704 AQs 0.6414 AQs 0.5886
77 0.6624 99 0.6335 99 0.5824
AQs 0.6621 AJs 0.6228 AQo 0.5675
AJs 0.6539 AQo 0.6227 AJs 0.5567
AKo 0.6532 ATs 0.6077 88 0.5534
ATs 0.6460 AJo 0.6026 AJo 0.5335
AQo 0.6443 88 0.6019 77 0.5266
AJo 0.6356 ATo 0.5865 ATs 0.5237
KQs 0.6340 A9s 0.5796 66 0.5056
66 0.6328 77 0.5756 ATo 0.4984
A9s 0.6278 KQs 0.5679 55 0.4858
ATo 0.6272 A8s 0.5603 A9s 0.4825
KJs 0.6257 A9o 0.5564 44 0.4635
A8s 0.6194 66 0.5535 KQs 0.4631
KTs 0.6179 KJs 0.5505 A8s 0.4551
KQo 0.6146 KQo 0.5448 A9o 0.4540
A7s 0.6098 A7s 0.5438 33 0.4411
A9o 0.6077 KTs 0.5359 KJs 0.4358
KJo 0.6057 A8o 0.5357 KQo 0.4340
55 0.6032 55 0.5336 A7s 0.4332
QJs 0.6026 A6s 0.5280 A8o 0.4245
K9s 0.5999 A5s 0.5263 A5s 0.4233
A5s 0.5992 KJo 0.5260 QJs 0.4201
A6s 0.5991 A7o 0.5181 A6s 0.4193
A8o 0.5987 A4s 0.5177 KTs 0.4192
KTo 0.5974 44 0.5114 22 0.4186
QTs 0.5947 A3s 0.5111 A4s 0.4154
A4s 0.5903 KTo 0.5104 QTs 0.4144
A7o 0.5884 K9s 0.5079 JTs 0.4125
K8s 0.5831 A2s 0.5042 A3s 0.4085
A3s 0.5822 A6o 0.5009 KJo 0.4049
QJo 0.5813 A5o 0.4991 A2s 0.4013
K9o 0.5781 QJs 0.4930 A7o 0.4010
A5o 0.5770 A4o 0.4899 T9s 0.3972
A6o 0.5768 33 0.4896 K9s 0.3947
Q9s 0.5766 A3o 0.4828 J9s 0.3923
K7s 0.5754 K8s 0.4808 Q9s 0.3922
JTs 0.5753 K9o 0.4805 A5o 0.3901
A2s 0.5738 QTs 0.4800 QJo 0.3881
QTo 0.5729 A2o 0.4753 KTo 0.3868
44 0.5702 22 0.4701 98s 0.3859
A4o 0.5673 K7s 0.4670 A6o 0.3856
K6s 0.5664 QJo 0.4651 T8s 0.3823
K8o 0.5602 JTs 0.4592 QTo 0.3820
Q8s 0.5602 K6s 0.4543 A4o 0.3815
A3o 0.5584 Q9s 0.4531 JTo 0.3802
K5s 0.5579 K8o 0.4515 87s 0.3787
J9s 0.5566 QTo 0.4512 J8s 0.3783
Q9o 0.5536 K5s 0.4435 Q8s 0.3781
JTo 0.5525 K7o 0.4367 K8s 0.3779
K7o 0.5519 K4s 0.4352 K6s 0.3757
A2o 0.5493 J9s 0.4325 76s 0.3753
K4s 0.5488 JTo 0.4293 K7s 0.3746
Q7s 0.5430 Q8s 0.4287 A3o 0.3741
K6o 0.5422 K3s 0.4286 97s 0.3724
K3s 0.5405 T9s 0.4267 65s 0.3707
T9s 0.5403 K2s 0.4234 86s 0.3706
J8s 0.5402 K6o 0.4229 K5s 0.3703
33 0.5369 Q9o 0.4223 T7s 0.3674
Q6s 0.5361 J8s 0.4128 Q6s 0.3670
Q8o 0.5360 K5o 0.4114 A2o 0.3662
K5o 0.5331 Q7s 0.4108 T9o 0.3641
J9o 0.5325 T8s 0.4097 K4s 0.3637
K2s 0.5321 98s 0.4090 96s 0.3637
Q5s 0.5277 Q6s 0.4066 J7s 0.3637
T8s 0.5233 K4o 0.4024 Q7s 0.3634
K4o 0.5233 87s 0.4014 54s 0.3622
J7s 0.5232 J9o 0.4008 Q5s 0.3618
Q4s 0.5186 Q5s 0.4001 75s 0.3605
Q7o 0.5177 J7s 0.3989 K9o 0.3603
T9o 0.5153 97s 0.3965 J9o 0.3591
J8o 0.5149 Q8o 0.3963 T6s 0.3586
K3o 0.5143 T7s 0.3959 Q9o 0.3586
Q6o 0.5102 76s 0.3959 K3s 0.3570
Q3s 0.5102 K3o 0.3953 85s 0.3555
98s 0.5080 T9o 0.3949 Q4s 0.3553

Note that A2o drops back down in relative value when you're up against the top 25% as opposed to the top 50%. All pairs below 99 also move up in (relative) value.

P.S. Sorry this is so ugly, but the posting software is ignoring the tabs in the data.

[dana33]

A very interesting thing happened when I tried to compute the self-balanced ranking against the top 10% of hands (top 17). The process does not converge to a single ordered set, but cycles through the following 4 ordered sets. After reaching the ordering in the last column, it cycles back to the first:

AA AA AA AA
KK KK KK KK
QQ QQ QQ QQ
JJ JJ JJ JJ
AKs TT AKs AKs
AKo AKs TT AKo
TT AKo AKo TT
AQs 99 99 99
99 AQs AQs AQs
AQo 88 88 AQo
88 AQo AQo 88
AJs 77 AJs AJs
77 AJs KQs KQs
KQs 66 77 ATs
66 KQs KJs KJs
55 KTs ATs 77
AJo QTs KTs AJo
44 JTs QJs 66
ATs KJs AJo 55
33 ATs A9s A9s
22 QJs JTs KQo
KJs T9s KQo 44
KTs AJo QTs QJs
QTs 55 A8s KTs
KQo K9s KJo JTs
JTs KQo 66 33
QJs Q9s ATo A5s
T9s J9s K9s ATo
A9s A9s A5s A8s

(I include only the top 30 or so hands above, and have omitted the probability figures.)

[eastbay]

[ QUOTE ]
A very interesting thing happened when I tried to compute the self-balanced ranking against the top 10% of hands (top 17). The process does not converge to a single ordered set, but cycles through the following 4 ordered sets. After reaching the ordering in the last column, it cycles back to the first:

AA AA AA AA
KK KK KK KK
QQ QQ QQ QQ
JJ JJ JJ JJ
AKs TT AKs AKs
AKo AKs TT AKo
TT AKo AKo TT
AQs 99 99 99
99 AQs AQs AQs
AQo 88 88 AQo
88 AQo AQo 88
AJs 77 AJs AJs
77 AJs KQs KQs
KQs 66 77 ATs
66 KQs KJs KJs
55 KTs ATs 77
AJo QTs KTs AJo
44 JTs QJs 66
ATs KJs AJo 55
33 ATs A9s A9s
22 QJs JTs KQo
KJs T9s KQo 44
KTs AJo QTs QJs
QTs 55 A8s KTs
KQo K9s KJo JTs
JTs KQo 66 33
QJs Q9s ATo A5s
T9s J9s K9s ATo
A9s A9s A5s A8s

(I include only the top 30 or so hands above, and have omitted the probability figures.)

[/ QUOTE ]

Neato. I thought that might happen at some % (actually I thought it might happen at any % until I verified otherwise for 50%).

This is cool, but, I think we're into the realm of academic uselessness now. I've probably been there awhile. [img]/images/graemlins/smile.gif[/img]

eastbay